Maths Olympiad Prep

Track / Stage 4 / 206 of 340 #466 of 1964

Problem 466

AMC 12 late, AIME early
Algebra Difficulty 4.8 Find the answer

For the quadratic equation in xx, x2+(m+1)x+2mx^{2}+(m+1) x+2 m =0=0, if it has two integer roots, then m=m= \qquad , and the roots of the equation are \qquad .

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

 9. 0 and 60,1,3,4\begin{array}{l}\text { 9. 0 and } 6 \text {, } \\ 0,-1,-3,-4 \text {. }\end{array}

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.